Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
304 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #31773906 | C2 | semidirect |
| 4. C2×#22576079 | C2 | semidirect |
| 5. #31773668 | C2 | semidirect |
| 6. C271⋊#338 | C2 | semidirect |
| 22. C2×Q16×C271 | C4 | semidirect |
| 23. C2×SD16×C271 | C4 | semidirect |
| 107. C271 | #1902 | semidirect |
| 120. C2×Q16 | Dic271 | semidirect |
| 121. C2×SD16 | Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774664 | 2 |
| #31773914 | 2 |
| #31773906 | 2 |
| C2×#22576079 | 2 |
| #31773668 | 2 |
| C271⋊#338 | 2 |
| C2×#137×C271 | 2 |
| #1902 | 271 |